npbbb_efficiency

Evaluates the A-efficiency of a nested partially balanced bipartite
 block design separately for its block and sub-block classifications. For each
 classification the A-efficiency is
 $$E = A^{\mathrm{opt}} / A,$$
 the ratio of the A-value of the A-optimal completely symmetric reference
 design to the A-value of the design under study. A value of <code>1</code> means the
 design is A-optimal for that classification. For more details see Vinayaka et
 al. (2026).

Construction and evaluation of nested partially balanced bipartite block (NPBBB) designs for comparing a set of test treatments with a set of control treatments under a nested (blocks within blocks) structure. Six systematic construction methods are provided: composing partially balanced bipartite block designs with nested balanced incomplete block designs; augmenting nested partially balanced incomplete block designs with controls; merging rows of group-divisible nested designs; direct construction from group-divisible schemes; and expansion of partially balanced incomplete block designs (Vinayaka et al. 2026: In press). The A-efficiencies of the block and sub-block classifications are computed against the A-optimal completely symmetric reference design, following the test-versus-control optimality framework of Gupta and Parsad (1996) <doi:10.1080/03610929608831743> and Vinayaka et al. (2024) <doi:10.1080/03610926.2023.2251623>. These designs are particularly suited to agricultural, animal husbandry, industrial, and clinical trials involving multiple standard checks under nested experimental conditions, such as multi-environment trials where field heterogeneity (blocks) and within-field variation (sub-blocks) must be controlled simultaneously.

Vinayaka 

NPBBBdesigns

Construction and a-Efficiency of Nested Partially Balanced
Bipartite Block Designs

Rajender Parsad

B.N. Mandal

L.N. Vinaykumar

Gopalareddy Krishnappa

npbbb_efficiency function

<dl><dt>block_design</dt>
<dd>A matrix whose rows are the blocks (each block being the
concatenation of its sub-blocks) and whose entries are treatment labels
<code>1, ..., v1</code> (test) and <code>v1 + 1, ..., v1 + v2</code> (control).</dd>
<dt>subblock_design</dt>
<dd>A matrix whose rows are the sub-blocks, with the same
labelling convention.</dd>
<dt>v1</dt>
<dd>Number of test treatments.</dd>
<dt>v2</dt>
<dd>Number of control treatments.</dd></dl>

Arguments

A-Efficiency of an NPBBB Design — npbbb_efficiency

<dl>

<dt>block_design</dt>
<dd>A matrix whose rows are the blocks (each block being the
concatenation of its sub-blocks) and whose entries are treatment labels
<code>1, ..., v1</code> (test) and <code>v1 + 1, ..., v1 + v2</code> (control).</dd>


<dt>subblock_design</dt>
<dd>A matrix whose rows are the sub-blocks, with the same
labelling convention.</dd>


<dt>v1</dt>
<dd>Number of test treatments.</dd>


<dt>v2</dt>
<dd>Number of control treatments.</dd>

</dl>

npbbb_efficiency: A-Efficiency of an NPBBB Design

Description

Usage

Value

Arguments

References

Examples